On cherche à étudier l’effet de trois facteurs sur le transcriptome des racines d’Arabidopsis thaliana et de la micro Tomate.

## corrplot 0.84 loaded

CO2

Clustering

****************************************
coseq analysis: Poisson approach & none transformation
K = 2 to 12 
Use set.seed() prior to running coseq for reproducible results.
****************************************
Running g = 2 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0"
Running g = 3 ...
[1] "Initialization: 1"
[1] "Log-like diff: 4.90653064844082e-08"
Running g = 4 ...
[1] "Initialization: 1"
[1] "Log-like diff: 9.85664883046411e-11"
Running g = 5 ...
[1] "Initialization: 1"
[1] "Log-like diff: 5.50989511793887e-08"
Running g = 6 ...
[1] "Initialization: 1"
[1] "Log-like diff: 1.78097423031431e-07"
Running g = 7 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0"
Running g = 8 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0"
Running g = 9 ...
[1] "Initialization: 1"
[1] "Log-like diff: 5.05190030253289e-07"
Running g = 10 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0"
Running g = 11 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0"
Running g = 12 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0"
$ICL


$profiles


$boxplots


$probapost_barplots


*************************************************
Model: Poisson
Transformation: none
*************************************************
Clusters fit: 2,3,4,5,6,7,8,9,10,11,12
Clusters with errors: ---
Selected number of clusters via ICL: 12
ICL of selected model: -740101.6
*************************************************
Number of clusters = 12
ICL = -740101.6
*************************************************
Cluster sizes:
 Cluster 1  Cluster 2  Cluster 3  Cluster 4  Cluster 5  Cluster 6  Cluster 7 
         9         12          1         22          6         24         12 
 Cluster 8  Cluster 9 Cluster 10 Cluster 11 Cluster 12 
         3          4         10         10         18 

Number of observations with MAP > 0.90 (% of total):
131 (100%)

Number of observations with MAP > 0.90 per cluster (% of total per cluster):
 Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Cluster 7
 9         12        1         22        6         24        12       
 (100%)    (100%)    (100%)    (100%)    (100%)    (100%)    (100%)   
 Cluster 8 Cluster 9 Cluster 10 Cluster 11 Cluster 12
 3         4         10         10         18        
 (100%)    (100%)    (100%)     (100%)     (100%)    

Model-Based Clustering Using MPLN (Parallelized) Description Performs clustering using mixtures of multivariate Poisson-log normal (MPLN) distribution and model selection using AIC, AIC3, BIC and ICL. Since each component/cluster size (G) is independent from another, all Gs in the range to be tested have been parallelized to run on a seperate core using the parallel R package.

Visualisation en ACP

Class: pca dudi
Call: dudi.pca(df = log(data + 0.1), center = TRUE, scale = TRUE, scannf = FALSE, 
    nf = 4)

Total inertia: 24

Eigenvalues:
    Ax1     Ax2     Ax3     Ax4     Ax5 
17.2861  4.7060  0.6320  0.5028  0.2615 

Projected inertia (%):
    Ax1     Ax2     Ax3     Ax4     Ax5 
 72.025  19.608   2.633   2.095   1.089 

Cumulative projected inertia (%):
    Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
  72.03   91.63   94.27   96.36   97.45 

(Only 5 dimensions (out of 24) are shown)

NULL

On essaie avec une ACP basée sur modèle Poisson Log Normal, de PNLModels :


 Initialization...

 Adjusting 10 PLN models for PCA analysis.
     Rank approximation = 1 
     Rank approximation = 2 
     Rank approximation = 3 
     Rank approximation = 4 
     Rank approximation = 5 
     Rank approximation = 6 
     Rank approximation = 7 
     Rank approximation = 8 
     Rank approximation = 9 
     Rank approximation = 10 
 Post-treatments
 DONE!
--------------------------------------------------------
COLLECTION OF 10 POISSON LOGNORMAL MODELS
--------------------------------------------------------
 Task: Principal Component Analysis
========================================================
 - Ranks considered: from 1 to 10
 - Best model (greater BIC): rank = 10 - R2 = 0.97
 - Best model (greater ICL): rank = 10 - R2 = 0.97

Réseau avec PLN Network


 Initialization...
 Adjusting 30 PLN with sparse inverse covariance estimation
    Joint optimization alternating gradient descent and graphical-lasso
    sparsifying penalty = 1.673463 
    sparsifying penalty = 1.545729 
    sparsifying penalty = 1.427745 
    sparsifying penalty = 1.318766 
    sparsifying penalty = 1.218106 
    sparsifying penalty = 1.125129 
    sparsifying penalty = 1.039249 
    sparsifying penalty = 0.9599238 
    sparsifying penalty = 0.8866536 
    sparsifying penalty = 0.8189761 
    sparsifying penalty = 0.7564644 
    sparsifying penalty = 0.6987241 
    sparsifying penalty = 0.6453911 
    sparsifying penalty = 0.5961289 
    sparsifying penalty = 0.5506269 
    sparsifying penalty = 0.508598 
    sparsifying penalty = 0.4697772 
    sparsifying penalty = 0.4339195 
    sparsifying penalty = 0.4007988 
    sparsifying penalty = 0.3702062 
    sparsifying penalty = 0.3419487 
    sparsifying penalty = 0.315848 
    sparsifying penalty = 0.2917396 
    sparsifying penalty = 0.2694714 
    sparsifying penalty = 0.2489028 
    sparsifying penalty = 0.2299043 
    sparsifying penalty = 0.2123559 
    sparsifying penalty = 0.196147 
    sparsifying penalty = 0.1811752 
    sparsifying penalty = 0.1673463 
 Post-treatments
 DONE!

Stability Selection for PLNnetwork: 
subsampling: ++++++++++++++++++++

[1] 431
[1] 476

Nitrate

Clustering

****************************************
coseq analysis: Poisson approach & none transformation
K = 2 to 12 
Use set.seed() prior to running coseq for reproducible results.
****************************************
Running g = 2 ...
[1] "Initialization: 1"
[1] "Log-like diff: 4.59017712728382e-10"
Running g = 3 ...
[1] "Initialization: 1"
[1] "Log-like diff: 1411.59027483396"
[1] "Log-like diff: 135.834263142698"
[1] "Log-like diff: 4.87166334779407"
[1] "Log-like diff: 0.163549842887022"
[1] "Log-like diff: 0.00440584508602626"
Running g = 4 ...
[1] "Initialization: 1"
[1] "Log-like diff: 1.21945280540103e-07"
Running g = 5 ...
[1] "Initialization: 1"
[1] "Log-like diff: 94.168448285313"
[1] "Log-like diff: 27.8326764519581"
[1] "Log-like diff: 0.0538298186603754"
[1] "Log-like diff: 0.00039741358597567"
[1] "Log-like diff: 5.95410822157305e-06"
Running g = 6 ...
[1] "Initialization: 1"
[1] "Log-like diff: 4.55134596677453e-10"
Running g = 7 ...
[1] "Initialization: 1"
[1] "Log-like diff: 2.99828419869641e-05"
[1] "Log-like diff: 1.15869511319033e-06"
Running g = 8 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0.00324992917408906"
[1] "Log-like diff: 8.9456142298161e-05"
[1] "Log-like diff: 7.87921585754248e-06"
Running g = 9 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0.0027331480212851"
[1] "Log-like diff: 3.20043587862529e-05"
[1] "Log-like diff: 4.71615422270588e-07"
Running g = 10 ...
[1] "Initialization: 1"
[1] "Log-like diff: 180.385205910929"
[1] "Log-like diff: 0.132498221681843"
[1] "Log-like diff: 0.000265799264397515"
[1] "Log-like diff: 3.29221322772355e-05"
[1] "Log-like diff: 5.96817702813723e-07"
Running g = 11 ...
[1] "Initialization: 1"
[1] "Log-like diff: 7.89839428474253"
[1] "Log-like diff: 0.914622663010462"
[1] "Log-like diff: 0.527449866368762"
[1] "Log-like diff: 0.244277441686506"
[1] "Log-like diff: 0.112796925842808"
Running g = 12 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0.00324309141651824"
[1] "Log-like diff: 0.000818172500085979"
[1] "Log-like diff: 0.000206378430380738"
[1] "Log-like diff: 5.20935887955432e-05"
[1] "Log-like diff: 1.31237750160551e-05"
$ICL


$profiles


$boxplots


$probapost_barplots


*************************************************
Model: Poisson
Transformation: none
*************************************************
Clusters fit: 2,3,4,5,6,7,8,9,10,11,12
Clusters with errors: ---
Selected number of clusters via ICL: 12
ICL of selected model: -3013888
*************************************************
Number of clusters = 12
ICL = -3013888
*************************************************
Cluster sizes:
 Cluster 1  Cluster 2  Cluster 3  Cluster 4  Cluster 5  Cluster 6  Cluster 7 
        63         98         74         47        103         38         21 
 Cluster 8  Cluster 9 Cluster 10 Cluster 11 Cluster 12 
       160          5         24        154         50 

Number of observations with MAP > 0.90 (% of total):
833 (99.52%)

Number of observations with MAP > 0.90 per cluster (% of total per cluster):
 Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Cluster 7
 63        98        74        47        103       37        21       
 (100%)    (100%)    (100%)    (100%)    (100%)    (97.37%)  (100%)   
 Cluster 8 Cluster 9 Cluster 10 Cluster 11 Cluster 12
 159       5         24         153        49        
 (99.38%)  (100%)    (100%)     (99.35%)   (98%)     

ACP

Class: pca dudi
Call: dudi.pca(df = log(data + 0.1), center = TRUE, scale = TRUE, scannf = FALSE, 
    nf = 4)

Total inertia: 24

Eigenvalues:
    Ax1     Ax2     Ax3     Ax4     Ax5 
19.1712  3.3535  0.5249  0.3943  0.1205 

Projected inertia (%):
    Ax1     Ax2     Ax3     Ax4     Ax5 
 79.880  13.973   2.187   1.643   0.502 

Cumulative projected inertia (%):
    Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
  79.88   93.85   96.04   97.68   98.18 

(Only 5 dimensions (out of 24) are shown)

NULL


 Initialization...

 Adjusting 10 PLN models for PCA analysis.
     Rank approximation = 1 
     Rank approximation = 2 
     Rank approximation = 3 
     Rank approximation = 4 
     Rank approximation = 5 
     Rank approximation = 6 
     Rank approximation = 7 
     Rank approximation = 8 
     Rank approximation = 9 
     Rank approximation = 10 
 Post-treatments
 DONE!
--------------------------------------------------------
COLLECTION OF 10 POISSON LOGNORMAL MODELS
--------------------------------------------------------
 Task: Principal Component Analysis
========================================================
 - Ranks considered: from 1 to 10
 - Best model (greater BIC): rank = 10 - R2 = 0.97
 - Best model (greater ICL): rank = 10 - R2 = 0.97

Relevance network

          degree betweenness Rank_stat
AT4G32950    168    4195.902    684.50
AT2G30660    177    3893.654    682.00
AT5G39130    157    4167.511    680.00
AT1G74590    163    3818.345    679.00
AT5G54370    182    3334.164    677.00
AT3G44300    136    7640.805    673.50
AT3G16180    147    3766.436    671.00
AT1G52070    136    4848.893    669.00
AT5G24070    134    3813.655    659.00
AT2G46680    166    2202.663    658.50
AT4G23400    152    2417.920    658.25
AT2G31880    130    4797.134    657.50
AT1G69490    159    2110.001    654.50
AT2G30670    146    2258.923    653.00
AT1G20180    153    1838.916    644.00
AT2G21880    127    3149.782    643.50
AT5G06730    164    1721.279    643.00
AT5G38900    122    3819.292    639.00
AT1G01680    135    2184.533    638.75
AT5G46890    162    1569.691    633.00
AT1G22530    124    2724.852    632.50
AT5G22270    130    2131.515    629.00
AT4G25250    113    4488.276    628.00
AT4G27400    134    1838.540    627.00
AT1G25400    140    1671.199    626.25
 [ reached 'max' / getOption("max.print") -- omitted 670 rows ]

PLN Ntework


 Initialization...
 Adjusting 30 PLN with sparse inverse covariance estimation
    Joint optimization alternating gradient descent and graphical-lasso
    sparsifying penalty = 1.07978 
    sparsifying penalty = 0.9973615 
    sparsifying penalty = 0.9212337 
    sparsifying penalty = 0.8509167 
    sparsifying penalty = 0.785967 
    sparsifying penalty = 0.7259748 
    sparsifying penalty = 0.6705618 
    sparsifying penalty = 0.6193784 
    sparsifying penalty = 0.5721018 
    sparsifying penalty = 0.5284337 
    sparsifying penalty = 0.4880988 
    sparsifying penalty = 0.4508427 
    sparsifying penalty = 0.4164302 
    sparsifying penalty = 0.3846445 
    sparsifying penalty = 0.3552849 
    sparsifying penalty = 0.3281663 
    sparsifying penalty = 0.3031176 
    sparsifying penalty = 0.2799809 
    sparsifying penalty = 0.2586102 
    sparsifying penalty = 0.2388707 
    sparsifying penalty = 0.2206379 
    sparsifying penalty = 0.2037968 
    sparsifying penalty = 0.1882412 
    sparsifying penalty = 0.1738729 
    sparsifying penalty = 0.1606013 
    sparsifying penalty = 0.1483428 
    sparsifying penalty = 0.1370199 
    sparsifying penalty = 0.1265613 
    sparsifying penalty = 0.116901 
    sparsifying penalty = 0.107978 
 Post-treatments
 DONE!

Stability Selection for PLNnetwork: 
subsampling: ++++++++++++++++++++

          degree betweenness Rank_stat
AT1G21240    158  16953.1888    400.00
AT1G33820    134  12667.9013    399.00
AT3G53770     95   3946.6477    397.00
AT5G55110    103   2920.1525    397.00
AT1G34047     57   4572.2856    395.50
AT4G27400     69   1640.9440    395.00
AT5G46890     63   1462.3665    394.00
AT1G33960     61    935.9150    391.00
AT1G10070     37   2611.7509    390.25
AT5G43590     55    966.5146    390.00
AT1G08430     47   1201.3616    389.50
AT4G32950     56    765.7225    389.00
AT1G52130     48    761.4761    387.00
AT2G41850     49    508.6514    387.00
AT2G23270     34   1081.6611    385.75
AT5G20790     35    889.9951    385.00
AT1G15125     28   1392.5802    384.50
AT1G51840     37    342.9828    381.75
AT1G01680     36    375.8168    381.50
AT2G30670     41    251.8479    380.50
AT2G45760     28    506.1166    380.00
AT2G40740     34    321.6113    379.25
AT1G63590     28    422.9557    379.00
AT4G24350     25    445.6824    376.50
AT5G35525     32    235.7482    374.50
 [ reached 'max' / getOption("max.print") -- omitted 375 rows ]

Iron

Clustering

****************************************
coseq analysis: Poisson approach & none transformation
K = 2 to 12 
Use set.seed() prior to running coseq for reproducible results.
****************************************
Running g = 2 ...
[1] "Initialization: 1"
[1] "Log-like diff: 1.06819442180495e-10"
Running g = 3 ...
[1] "Initialization: 1"
[1] "Log-like diff: 6.38532489389831e-05"
[1] "Log-like diff: 6.09656783900903e-06"
Running g = 4 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0.0111170800072813"
[1] "Log-like diff: 0.00141139826298442"
[1] "Log-like diff: 0.000161397428641408"
[1] "Log-like diff: 2.2397745002678e-05"
[1] "Log-like diff: 2.78974421874523e-06"
Running g = 5 ...
[1] "Initialization: 1"
[1] "Log-like diff: 0.0387118669603943"
[1] "Log-like diff: 0.00732243729624926"
[1] "Log-like diff: 0.00136628427148366"
[1] "Log-like diff: 0.000246221735089591"
[1] "Log-like diff: 4.5249045658835e-05"
Running g = 6 ...
[1] "Initialization: 1"
[1] "Log-like diff: 1091.54513354431"
[1] "Log-like diff: 384.306342804397"
[1] "Log-like diff: 471.016220532387"
[1] "Log-like diff: 427.086443409924"
[1] "Log-like diff: 664.326791316329"
Running g = 7 ...
[1] "Initialization: 1"
[1] "Log-like diff: 427.257427847843"
[1] "Log-like diff: 680.01581885371"
[1] "Log-like diff: 1786.85942209259"
[1] "Log-like diff: 1583.70876190583"
[1] "Log-like diff: 303.739086114212"
Running g = 8 ...
[1] "Initialization: 1"
[1] "Log-like diff: 241.58230457968"
[1] "Log-like diff: 364.01646505909"
[1] "Log-like diff: 398.598735924692"
[1] "Log-like diff: 2.65393254768138"
[1] "Log-like diff: 112.913902215817"
Running g = 9 ...
[1] "Initialization: 1"
[1] "Log-like diff: 416.451620701424"
[1] "Log-like diff: 358.536512856528"
[1] "Log-like diff: 51.7726131046729"
[1] "Log-like diff: 281.540823604593"
[1] "Log-like diff: 92.5768743207845"
Running g = 10 ...
[1] "Initialization: 1"
[1] "Log-like diff: 24.1783541782546"
[1] "Log-like diff: 17.4979676949227"
[1] "Log-like diff: 1.99520130713022"
[1] "Log-like diff: 23.5706044092903"
[1] "Log-like diff: 4.05590908308703"
Running g = 11 ...
[1] "Initialization: 1"
[1] "Log-like diff: 1212.67923420344"
[1] "Log-like diff: 1457.72471004209"
[1] "Log-like diff: 798.015375131625"
[1] "Log-like diff: 275.736282250256"
[1] "Log-like diff: 30.0350562940232"
Running g = 12 ...
[1] "Initialization: 1"
[1] "Log-like diff: 670.628345670554"
[1] "Log-like diff: 334.935422347285"
[1] "Log-like diff: 325.249048271772"
[1] "Log-like diff: 393.053680612322"
[1] "Log-like diff: 71.9330493252254"
$ICL


$profiles


$boxplots


$probapost_barplots


*************************************************
Model: Poisson
Transformation: none
*************************************************
Clusters fit: 2,3,4,5,6,7,8,9,10,11,12
Clusters with errors: ---
Selected number of clusters via ICL: 12
ICL of selected model: -3391000
*************************************************
Number of clusters = 12
ICL = -3391000
*************************************************
Cluster sizes:
 Cluster 1  Cluster 2  Cluster 3  Cluster 4  Cluster 5  Cluster 6  Cluster 7 
       107        164         30        638        337         43        433 
 Cluster 8  Cluster 9 Cluster 10 Cluster 11 Cluster 12 
       196        122         51        113        607 

Number of observations with MAP > 0.90 (% of total):
2769 (97.47%)

Number of observations with MAP > 0.90 per cluster (% of total per cluster):
 Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Cluster 7
 98        158       28        626       328       40        421      
 (91.59%)  (96.34%)  (93.33%)  (98.12%)  (97.33%)  (93.02%)  (97.23%) 
 Cluster 8 Cluster 9 Cluster 10 Cluster 11 Cluster 12
 195       118       51         107        599       
 (99.49%)  (96.72%)  (100%)     (94.69%)   (98.68%)  

 Initialization...

 Adjusting 10 PLN models for PCA analysis.
     Rank approximation = 1 
     Rank approximation = 2 
     Rank approximation = 3 
     Rank approximation = 4 
     Rank approximation = 5 
     Rank approximation = 6 
     Rank approximation = 7 
     Rank approximation = 8 
     Rank approximation = 9 
     Rank approximation = 10 
 Post-treatments
 DONE!
--------------------------------------------------------
COLLECTION OF 10 POISSON LOGNORMAL MODELS
--------------------------------------------------------
 Task: Principal Component Analysis
========================================================
 - Ranks considered: from 1 to 10
 - Best model (greater BIC): rank = 10 - R2 = 0.96
 - Best model (greater ICL): rank = 10 - R2 = 0.96

ACP

Class: pca dudi
Call: dudi.pca(df = log(data + 0.1), center = TRUE, scale = TRUE, scannf = FALSE, 
    nf = 4)

Total inertia: 24

Eigenvalues:
     Ax1      Ax2      Ax3      Ax4      Ax5 
22.01676  1.12356  0.26987  0.11457  0.06979 

Projected inertia (%):
    Ax1     Ax2     Ax3     Ax4     Ax5 
91.7365  4.6815  1.1245  0.4774  0.2908 

Cumulative projected inertia (%):
    Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
  91.74   96.42   97.54   98.02   98.31 

(Only 5 dimensions (out of 24) are shown)

NULL

Relevance network

          degree betweenness Rank_stat
AT5G51070     59   2085.0820    278.50
AT5G53350     46   5251.7184    277.50
AT5G27350     53   1343.7899    271.50
AT5G24810     45   1625.2303    270.25
AT1G16120     57   1211.4976    269.50
AT3G59210     41   1847.0837    269.50
AT4G21534     41   1686.1707    268.50
AT5G60530     48   1185.7926    267.00
AT4G30790     52    781.6829    262.50
AT1G09935     41   1140.4143    261.00
AT3G49490     26   2830.0678    259.50
AT3G25660     32   1379.9615    259.25
AT1G50430     26   1986.4049    256.50
AT5G44510     46    663.6271    255.50
AT5G13710     30   1272.7125    255.25
AT3G03890     45    667.0113    254.25
AT5G14420     50    586.0264    252.50
AT5G40010     46    584.1702    250.50
AT4G04920     35    774.2882    250.50
AT3G09960     39    652.8921    249.25
AT5G08660     42    541.1541    245.50
AT1G51470     34    630.4088    245.00
AT4G23850     39    566.8410    244.25
AT4G24760     33    610.1257    244.00
AT4G22740     16   7769.8295    243.00
 [ reached 'max' / getOption("max.print") -- omitted 257 rows ]

PLN Network


 Initialization...
 Adjusting 30 PLN with sparse inverse covariance estimation
    Joint optimization alternating gradient descent and graphical-lasso
    sparsifying penalty = 1.240511 
    sparsifying penalty = 1.145824 
    sparsifying penalty = 1.058364 
    sparsifying penalty = 0.9775802 
    sparsifying penalty = 0.9029624 
    sparsifying penalty = 0.83404 
    sparsifying penalty = 0.7703785 
    sparsifying penalty = 0.7115761 
    sparsifying penalty = 0.6572621 
    sparsifying penalty = 0.6070939 
    sparsifying penalty = 0.5607549 
    sparsifying penalty = 0.517953 
    sparsifying penalty = 0.4784181 
    sparsifying penalty = 0.4419008 
    sparsifying penalty = 0.4081709 
    sparsifying penalty = 0.3770156 
    sparsifying penalty = 0.3482383 
    sparsifying penalty = 0.3216576 
    sparsifying penalty = 0.2971057 
    sparsifying penalty = 0.2744279 
    sparsifying penalty = 0.2534811 
    sparsifying penalty = 0.2341331 
    sparsifying penalty = 0.2162619 
    sparsifying penalty = 0.1997548 
    sparsifying penalty = 0.1845077 
    sparsifying penalty = 0.1704244 
    sparsifying penalty = 0.157416 
    sparsifying penalty = 0.1454006 
    sparsifying penalty = 0.1343023 
    sparsifying penalty = 0.1240511 
 Post-treatments
 DONE!

Stability Selection for PLNnetwork: 
subsampling: ++++++++++++++++++++

IGRAPH fc0e129 UNW- 400 474 -- 
+ attr: name (v/c), label (v/c), label.cex (v/n), size (v/n),
| label.color (v/c), frame.color (v/l), weight (e/n), color (e/c),
| width (e/n)
+ edges from fc0e129 (vertex names):
 [1] AT4G36820--AT1G10070 AT4G36820--AT5G38910 AT4G36820--AT5G66890
 [4] AT4G36820--AT3G48740 AT4G36820--AT1G55790 AT4G36820--AT3G02150
 [7] AT4G36820--AT2G19500 AT4G36820--AT3G53770 AT4G36820--AT2G25625
[10] AT1G51470--AT5G38910 AT1G51470--AT1G47600 AT1G51470--AT3G53770
[13] AT1G51470--AT1G50720 AT1G65500--AT5G38910 AT1G65500--AT5G66890
[16] AT1G65500--AT1G09935 AT1G65500--AT5G09570 AT1G65500--AT5G10760
+ ... omitted several edges

 Initialization...
 Adjusting 30 PLN with sparse inverse covariance estimation
    Joint optimization alternating gradient descent and graphical-lasso
    sparsifying penalty = 1.240511 
    sparsifying penalty = 1.145824 
    sparsifying penalty = 1.058364 
    sparsifying penalty = 0.9775802 
    sparsifying penalty = 0.9029624 
    sparsifying penalty = 0.83404 
    sparsifying penalty = 0.7703785 
    sparsifying penalty = 0.7115761 
    sparsifying penalty = 0.6572621 
    sparsifying penalty = 0.6070939 
    sparsifying penalty = 0.5607549 
    sparsifying penalty = 0.517953 
    sparsifying penalty = 0.4784181 
    sparsifying penalty = 0.4419008 
    sparsifying penalty = 0.4081709 
    sparsifying penalty = 0.3770156 
    sparsifying penalty = 0.3482383 
    sparsifying penalty = 0.3216576 
    sparsifying penalty = 0.2971057 
    sparsifying penalty = 0.2744279 
    sparsifying penalty = 0.2534811 
    sparsifying penalty = 0.2341331 
    sparsifying penalty = 0.2162619 
    sparsifying penalty = 0.1997548 
    sparsifying penalty = 0.1845077 
    sparsifying penalty = 0.1704244 
    sparsifying penalty = 0.157416 
    sparsifying penalty = 0.1454006 
    sparsifying penalty = 0.1343023 
    sparsifying penalty = 0.1240511 
 Post-treatments
 DONE!

Stability Selection for PLNnetwork: 
subsampling: ++++++++++++++++++++

          degree betweenness Rank_stat
AT5G38910    132  9618.96649    400.00
AT5G09570     58  1788.52677    399.00
AT5G66890     42   669.82971    398.00
AT3G53770     41   407.52131    396.50
AT4G23140     25   490.16940    395.50
AT1G50720     31   390.03074    395.50
AT2G25625     26   356.60922    394.50
AT3G48740     19   301.23424    392.00
AT1G10070     18   313.16554    391.75
AT5G10760     18   220.20171    389.75
AT4G10860     24   132.89718    388.00
AT3G42550     14   184.38693    387.75
AT5G46960     16   147.88541    386.50
AT4G27150     12   164.55921    385.25
AT5G16970     10   278.10093    385.25
AT4G01390     11   176.83155    384.75
AT1G47600     14    62.48665    383.25
AT2G19500     12    46.05371    380.75
AT5G43650      9    75.01898    379.00
AT1G09935     11    43.04814    378.75
AT1G55790      9    46.20298    377.00
AT5G46610     11    31.25905    375.75
AT1G13310     10    33.40311    375.25
AT2G15880      5   230.57348    375.25
AT4G36820      9    37.74033    374.50
 [ reached 'max' / getOption("max.print") -- omitted 375 rows ]

Meeting summary Antoine Sophie

Enquête sur la similarité entre cNF et CNF

  • Corrélations entre les réplicats à l’intérieur d’une condition et de l’autre sont faiblement supérieures à celles entre cNF et CNF (images investigations factorCO2)
Réseau CO2

Réseau CO2

  • Quand on compare CNF à une condition x et cNF à cette même condition x (6 conditions possibles pour x), on retrouve entre 40 et 70% de gènes en commun, suggérant toute fois des différences entre ces deux transcritômes (on aurait presque 100% de similarité sinon)

Application des ces méthodes à la tomate

  • La tomate semble répondre différemment dans certaines mesures : plus d’effet du CO2, effet moindre du fer, effet nitrate plutôt similaire.

  • Ontologies moins fournies pour la tomate

Réseau CO2

Réseau CO2

Relevance network sur les gènes qui répondent globalement à un facteur

  • DEG en commun entre les 4 comparaisons possibles pour l’effet d’un facteur (Venn diagrams)

  • Fait sur l’ensemble des transcriptômes (plus large que les transcriptômes sur lesquels les DEG ont été détectés)

  • Relevance Network fait comme Rodrigo. et Al, seuil sur la valeur de corréation et sur la pvalue, gènes triés sur leur centralité et connectivité

  • Visualisés dans igraph après Clustering

  • Visualisés dans Cytoscape, pus clustering de communautés (pluggins) et analyse d’enrichissement d’ontologies

Réseau CO2

Réseau CO2

Début de biblio sur les méthodes d’inférence de GRN

  • Regression: Transcription factors are selected by target gene specific sparse linear regression and data resampling approaches.

  • Bayesian networks optimize posterior probabilities by different heuristic searches.

  • Correlation Edges are ranked based on variants of correlation.

  • Méthodes mixtes Consensus entre différentes techniques (conclusion de la métanalyse et benchmarcks du projet DREAM5 (wisdom of crowds))

Others : Genie3: A random forest, neural networks, chi 2 - Mutual Information: Edges are (1) ranked based on variants of mutual information and (2) filtered for causal relationships.

GGM Inference Notes :

The better should be to infer one network per condition, but as data is scarce, we’d rather use all conditions for one network : multitask learning

Assumptions :

  • Few interaction : sparse adj matrix

  • Networks are structured

Partial correlation : correlation between two genes knowing all the others. Indep ssi partial corr \(= 0\).

The general principle is to optimize a likelihood function (probability of the data given a set of parameters \(\Theta\)) minus a penalty imposing the disered assumptions, tuned by \(\lambda\) (kind of prior). Penalty enables : regularisation for high number of genes, selection for sparsity, and model driven inference.

Cette function à optimiser peut varier :

-MeinHousen and Bulhman (2006)

Si \(X_i\) est un vecteur de \(X\), alors on écrit \(X_i = X_{\i}\beta + \epsilon\) On essaie de prédire l’expression d’un gène avec tous les autres, avec \(\beta_j=- \frac{\theta_{ij}}{\theta_{ij}}\).

 

A work by Océane Cassan

oceane.cassan@supagro.fr